There are people all over town who will let you park your boat at their pier. But (to my knowledge) there are no true "marinas" anywhere on Ambergris Caye, meaning full service facilities that offer electrical hookups, showers, disposal, and most importantly, security.
The Belize Yacht Club markets itself as having a "marina" but the amount of money they are asking for practically no services is outrageous.
Security is a big issue, boats walk, sail and motor away all by themselves often, from what I have heard. Boat motors walk off the boats often too.
I would not leave an expensive boat docked on Ambergris Caye unless I was living aboard or paying someone to watch it 24 hours a day. And I would lock everything of value away on it.
You might want to contact the TMM office and ask them who is watching their boats for them (they may have an employee doing this) and see if you can negotiate something with them to watch yours. I have no idea if they would do this or not or what they would charge.
If you are looking for a sailboat in the area, you might want to try the Rio Dulce website, there are two boat brokers advertising there and they have quite a few boats for sale. Go to www.mayaparadise.com